Multiplicative inverses for elements in field

How to compute multiplicative inverses for elements in any simple (not extended) finite field? I mean an algorithm which can be implemented in software.

Answer

The unit group of the finite field of order $q$ is a cyclic group of order $q-1.$ Thus, for any $a \in \mathbb{F}_q^{\times},$ $$a^{-1} = a^{q-2}.$$